Rotate object texture
The way of doing it with simple (non-UV) texture mapping, is to tweak the mapping coordinate and scale. 



For example: 


Switching X and Y axis, and scaling X by -1 will rotate the texture 90 degrees clockwise.
Switching X and Y axis, and scaling Y by -1 will rotate the texture 90 degrees counter-clockwise.
Scaling X and Y by -1 will flip the image vertically.


But you see that it's quite limiting, less intuitive and flexible than UV-map based rotation, described in gandalf3's answer.